Given a real interval $I$, are there standard name and notation for the vector space $\{f\in C^1(I)\,:\,f'\,\mathrm{is}\,\mathrm{absolutely}\,\mathrm{continuous}\}$?
I would guess $C^1_{a.c.}$ but I'm not sure if it is a widely used notation or if it requires to be defined explicitely.
And what about the spaces $\{f\in C^n(I)\,:\,f^{(n)}\,\mathrm{is}\,\mathrm{absolutely}\,\mathrm{continuous}\}$?